Paper Info
Title
Laplace Transforms of a Family of Functions Related to Quadratic Phase Function
Abstract
A parametric family of complex valued functions in the form of quadratic exponents are defined starting from the real valued Gaussian function. The family of functions include the quadratic phase function, which is also called the two-sided complex chirp. It is proven using contour integrals on the complex plane that the Laplace transforms of these functions are also complex valued quadratic exponents; the region of convergence of the Laplace transform include the entire <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$s$ </tex-math></inline-formula> -plane for finite <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$|s|$ </tex-math></inline-formula> for a range of values of the defining parameter of the family. Fourier transforms are also presented as the special cases of the Laplace transform.
Year
DOI
Venue
2022
10.1109/TCSII.2022.3189591
IEEE Transactions on Circuits and Systems II: Express Briefs
Keywords
DocType
Volume
Laplace transform,quadratic phase function,two-sided chirp
Journal
69
Issue
ISSN
Citations 
11
1549-7747
0
PageRank 
References 
Authors
0.34
6
1
Name
Order
Citations
PageRank
Levent Onural111016.83